Deutsche Mark–Dollar Volatility: Intraday Activity...

Deutsche Mark–Dollar Volatility:Intraday Activity Patterns,

Macroeconomic Announcements,and Longer Run Dependencies

TORBEN G. ANDERSEN and TIM BOLLERSLEV*

ABSTRACT

This paper provides a detailed characterization of the volatility in the deutschemark–dollar foreign exchange market using an annual sample of five-minute re-turns. The approach captures the intraday activity patterns, the macroeconomicannouncements, and the volatility persistence (ARCH) known from daily returns.The different features are separately quantified and shown to account for a sub-stantial fraction of return variability, both at the intraday and daily level. Theimplications of the results for the interpretation of the fundamental “driving forces”behind the volatility process is also discussed.

THE EFFICIENT MARKET HYPOTHESIS contends that financial asset prices providerational assessments of fundamental values and future payoffs. By implica-tion, price changes should reflect the arrival and processing of all relevantnew information. However, the proportion of return variability that can beascribed to public news announcements is low. For example, Cutler, Poterba,and Summers (1989) find that even the largest daily price changes in thestock market generally cannot be associated with any significant economicnews.1 Moreover, proxies for the flow of public information, e.g., the numberof news items released by Reuter’s News Service (Berry and Howe (1994)) orDow Jones & Company (Mitchell and Mulherin (1994)) explain little of theoverall variation. Thus, if private information is ruled out, proponents ofrational price formation have to assert the existence of important news items

*Andersen is at the J.L. Kellogg Graduate School of Management, Northwestern University.Bollerslev is with the Department of Economics, University of Virginia. We are grateful forfinancial support from the Institute for Quantitative Research in Finance (the Q-Group). Spe-cial thanks are also due to Olsen and Associates for making the foreign exchange quotes avail-able. Furthermore, we have received valuable comments from seminar participants atNorthwestern University, University of Chicago, University of Houston, University of Windsor,Pennsylvania State University, the NBER Universities Research Conference on the Determi-nation of Exchange Rates, and the Econometric Society Summer Meetings in Iowa City. We arein particular indebted to comments from Mike Fishman, John Heaton, Bob Hodrick, TakatoshiIto, Ken Kavajecz, Richard Lyons, Bruce Mizrach, an anonymous referee, and the editor, RenéStulz. Needless to say, we remain fully responsible for the content.

1 The evidence is not much more encouraging for commodities whose aggregate supply isrelatively transparent (Roll (1984)), or, perhaps less surprisingly, at the individual firm level,where private information may be more prevalent (Roll (1988)).

THE JOURNAL OF FINANCE • VOL LIII, NO. 1 • FEBRUARY 1998

219

that may be discerned by market agents, but not by economists. This ispossible, but hardly convincing, and French and Roll (1986) provide strongevidence to the contrary. They document that return volatility is higher dur-ing trading than nontrading periods, independent of the flow of public news.They ascribe this to private information that is incorporated into prices throughtrading. One may, however, reiterate the question: What type of private in-formation can individuals obtain that is relevant to the pricing of broadassets, while not being readily available to other investors and, even ex post,not being discernible to outside observers?

Furthermore, as stressed by Goodhart and O’Hara (1996), any satisfactoryexplanation for the behavior of volatility based on the private informationhypothesis must be able to accommodate the striking empirical regularitiesin return volatility, not only over regular trading versus nontrading periods,but also within the trading day, within the trading week and over holidayperiods. Moreover, a full account of the process governing price variabilitymust also confront the pronounced volatility clustering, or ARCH effects,that are evident at the interday level. The one common observation acrossthese dimensions is that “market activity” is strongly correlated with pricevariability. Trading volume, return volatility, and bid–ask spreads are high-est around the open and close of trading; return variability per unit of timeis higher over trading than nontrading periods; trading volume and spreadsare particularly high on days with large return innovations; and public in-formation releases—which theoretically may induce price jumps without anytrading—are typically associated with extremely heavy volume.

Unfortunately, most empirical work has studied each of the abovephenomena—the intraday and intraweekly patterns (calendar effects), theannouncements (public information effects), and the interday volatility per-sistence (ARCH effects)—in isolation. This is ultimately not satisfactory.First, the similarity of the basic attributes across these dimensions sug-gests that there is a common component to the behavior which should beexplicitly accounted for in any rationalization of the volatility process. Sec-ond, real-time decision-making requires that the agents recognize the var-ious factors that exert a significant impact on current price movements.Since the factors display widely different stochastic properties, a decompo-sition of the contemporaneous effects is necessary in order to forecast vol-atility, even for the near future. Third, to judge the economic significanceof the findings, it is important to gauge the influence of the features atdifferent horizons. For example, the allocational role of the market, argu-ably, hinges on the information conveyed by prices at daily or lower fre-quencies, while studies of the market mechanism or institutions must payclose attention to the higher frequency patterns.

This paper takes a step in the direction called for above by providing acomprehensive characterization of the volatility process in the deutsche mark(DM)–dollar foreign exchange market based on a one-year sample of five-minute returns extracted from quotes on the Reuters interbank network.Although our emphasis is on the empirical identification of the various fac-

220 The Journal of Finance

tors and their relative impact at different frequencies, we also stress theimplications for theories of rational price fluctuations. The spot DM–dollarmarket constitutes a near ideal setting. It is the world’s largest market mea-sured by turnover, it is highly liquid, and it has low transaction costs. More-over, it is linked globally through computerized information systems, so newsis transmitted almost instantaneously to all participants. Further, it is a24-hour market composed of sequential and partially overlapping trading inregional centers worldwide, so it has no definite closures, except those gen-erated endogenously by the market. This allows for the study of the volatil-ity process over periods that would be nontrading intervals under centralizedmarket structures, thus including all public announcements, both in the UnitedStates and Germany, most of which fall outside the trading hours of theorganized stock exchanges.

Our main findings are as follows: First, contrary to Cutler et al. (1989), butconsistent with Ederington and Lee (1993), we show that the largest returnsappear linked to the release of public information, and, in particular, certainmacroeconomic announcements. Nonetheless, we conclude that these effectsare secondary when explaining overall volatility. The major announcements dom-inate the picture immediately following the release, but their explanatory poweris less than that of the intraday pattern at the high frequencies, and much lessthan that of standard volatility forecasts at the daily level. Thus, high-frequencydata are critical for identification of news that impacts the market, but theserather spectacular episodes do not explain what generally “drives” markets.Second, the most significant U.S. announcements, namely the employment re-port, gross domestic product, trade balance figures, and durable goods orders,are all related to the real economy, while the important German announce-ments, the Bundesbank meetings and M3 supply figures, are monetary. Thismay reflect differences in the (perceived) central bank reaction functions, orthat, over the sample period, monetary policy in the United States was stable,while in Germany it was highly controversial. Third, the clustering of publicinformation releases on certain weekdays explains the day-of-week effect. Hence,if announcement effects are ignored, day-dummies provide biased predictionsof excess volatility on specific weekdays. For days with important scheduledannouncements, such dummies fail to capture the full elevation in volatility,but the volatility will be exaggerated when no announcements are pending.Fourth, the significant calendar effects include a distinct intraday volatilitypattern, reflecting the daily activity cycle of the regional centers, as well as strongholiday, weekend, Daylight Saving Time, and Tokyo market opening effects.As a group, the calendar effects are the most important determinant of overallvolatility at the highest frequencies. Fifth, standard ARCH effects permeateintraday returns. Not only are these effects identifiable, but the high-frequencydata provide novel insights into this long-run component of volatility. For ex-ample, return variability over a given day is typically measured by the dailyabsolute (squared) return, but we find that procedures exploiting the entiresequence of intraday returns provide much improved measurements. In ad-dition, the interday ARCH component displays dependencies of the so-called

Deutsche Mark–Dollar Volatility 221

long-memory variety. This is an important result. Such features have been doc-umented at daily and lower frequencies, but their origin has been much de-bated. For instance, it has been argued that infrequent exogenous shifts in thevolatility process induces long-memory characteristics. Using daily data, theseexplanations are difficult to distinguish empirically. However, the presence oflong-memory characteristics in high-frequency returns, covering a short timespan, indicates that this feature is intrinsic to the system and not an artifactof exogenous shocks.

The empirical findings also have important implications for our under-standing of the forces that determine the intensity of price movements.First, the pronounced activity pattern in intraday volatility suggests a sig-nificant role for the trading process itself. For trading to be informative,there must be an element of asymmetric information present in the mar-ket. Lyons (1995, 1997) develops a model of the interbank market in whichdealers extract (private) signals from their customer (nondealer) order flow.This is rational if order flows speak to economic developments that onlybelatedly show up in statistics such as the trade balance and internationalcapital flows. However, the aggregate net customer order flow is the vari-able of primary interest, and dealers only get to interpret the fraction ofoverall orders they receive individually. Because dealers also have a stronginventory control motive for trade, interdealer trade will not reveal, orperfectly aggregate, the information in order flows. In such settings, mul-tiple trading rounds may be informative, even in the absence of additionalnews (see, e.g., Grundy and McNichols (1989), Brown and Jennings (1989),and Foster and Viswanathan (1996)). Moreover, most models stipulate thatthe precision of the information held by the different type of agents iscommon knowledge. If this assumption is relaxed, rational models againpredict that the trading process provides a useful tool for inference aboutthe structure and quality of the dispersed economy-wide information; see,e.g., Jacklin, Kleidon, and Pfleiderer (1992) and Romer (1993) for mostlytheoretical arguments, and Peiers (1997) for an empirical investigation intoBundesbank interventions in the foreign exchange market.

Second, Hsieh and Kleidon (1996) document that return volatility and bid–ask spreads extracted from quotes pertaining to specific regional segmentsof the interbank market obey the usual u-shaped patterns that have beenrationalized by clustering of informed trading (see, e.g., Admati and Pfleiderer(1988)). However, other regional segments, in the midst of their trading ses-sions, do not display any trace of a u-shape at the corresponding point intime. Hence, the regional u-shapes do not reflect particularly informativetrading during the opening or closing hours, but may, instead, constitute arational response to the abrupt changes in dealer exposure that occur asdealers periodically withdraw from the market place (see, e.g., Brock andKleidon (1992) and Hong and Wang (1995)). In addition, the necessity ofgetting a “feel” for the market before engaging in active trading is cited asan explanation for the early parts of the regional u-shape by Hsieh and


Kleidon (1996). This is, of course, consistent with the importance of learningdirectly from the trading process.

Third, public information arrivals induce abrupt price changes, but theaverage price move is typically attained within minutes. Still, volatility andtrading volume remain elevated for several hours (see, e.g., Kim and Ver-recchia (1991)). If agents have identical information sets and interpret newssimilarly, the protracted response pattern is hard to explain, and as suchprovides yet another argument in favor of models with heterogeneously in-formed agents.

Finally, the long-memory characteristics of the volatility process speak tothe potential importance of long-run persistence in the fundamental forcesgoverning the price process. It is hard to imagine that one may rationalizesuch features without relying on strong dependence in the processes deter-mining the rate of information flow and0or (private) order flow, and the as-sociated degree of uncertainty regarding the state of the underlying economicsystem. On the other hand, it is clear that a study of high-frequency returnsover a one-year sample can only address the issue indirectly. The origin oflonger run volatility persistence remains an important topic for future research.

The paper is structured as follows. Section I reports on the data sourcesand the construction of the five-minute return series. Section II provides apreliminary data analysis. A robust regression procedure for estimation ofthe calendar and announcement effects is developed in Section III, and Sec-tion IV summarizes the empirical evidence with an emphasis on the instan-taneous as well as the cumulative impact of each component. Section V assessesthe explanatory power of the volatility factors for intraday and daily returnvariability. Section VI concludes. An appendix, available at the Journal ofFinance web site, contains further discussion of the technical aspects of theestimation procedure.

I. Data Sources and Construction

Our primary data set consists of five-minute returns for the deutsche mark–dollar (DM–$) spot exchange rate from October 1, 1992, through September30, 1993.2 In addition, we utilize a longer daily time series of 3,649 spotDM–$ exchange rates from March 14, 1979, through September 29, 1993.The five-minute returns are constructed from the DM–$ exchange rate quotesthat appear on the interbank Reuters network over the sample period. Eachquote contains a bid and an ask price along with the time to the nearesteven second. At the end of each five-minute interval, we use the immediately

2 Going to a finer sampling interval results in the bid–ask bounce effect becoming dominant,as evidenced by the increasingly significant negative sample autocorrelations reported in Guil-laume et al. (1995). These findings are also consistent with the standard deviation of our five-minute return series being slightly less than the average quoted spread (see Bollerslev andMelvin (1994)).


preceding and following quote to construct the relevant bid and ask prices.The quotes are weighted by their inverse relative distance to the endpoint,and the log-price, log~Pt,n!, is then defined as the midpoint of the logarithmicbid and ask. The nth return within day t, Rt,n, is the change in log-pricesduring the corresponding period. All N 5 288 intervals during the 24-hourcycle are used. However, to avoid confounding the evidence by the decidedlyslower trading patterns over the weekends, all returns from Friday 21:00Greenwich Mean Time (GMT) through Sunday 21:00 GMT were excluded;see Bollerslev and Domowitz (1993) for an analysis of the interbank quoteactivity that justifies this “weekend” definition. To maintain a fixed numberof returns over the span of one week, we do not remove any observations dueto worldwide or country-specific holidays, although we control explicitly fortheir impact in the analysis below. This leaves us with a sample of T 5 260weekdays for a total of 74,880 five-minute return observations; i.e., Rt,n,n 5 1,2, . . . , N, t 5 1,2, . . . ,T. The data set also includes all of the news head-lines that appeared on the Reuters money news-alert screens. During thesample period from October 1, 1992 through September 30, 1993, a total of105,065 such headlines appeared. These are time stamped to the second andconstitute the basis for our analysis of announcement effects.

II. Preliminary Data Analysis

This section provides an initial investigation of our high-frequency foreignexchange return series that serves to motivate our formal model in Sec-tion III. It falls naturally in three parts, corresponding to each of the generalfactors that we identify as important determinants of the volatility process.

A. Daily ARCH Effects

Market microstructure theories concerning the relation between informa-tion flow, return volatility, and trading activity often ignore the lower fre-quency movements in volatility that are associated with the conditionalheteroskedasticity of daily returns. This is probably related to the fact that,until recently, empirical studies have been unable to document that intradayreturn volatility displays characteristics that are consistent with those ob-served at the lower frequencies. At the face of it, this is utterly puzzling.How can the intraday return volatility process be void of ARCH featureswhen the identical data, aggregated to the daily level, provide overwhelmingevidence of conditional heteroskedasticity? An answer is provided by Ander-sen and Bollerslev (1997a) who demonstrate that the strong intraday vola-tility pattern interferes with, and garbles, the time series structure of interdayvolatility. Only by explicitly modeling the intraday pattern is it possible torecover meaningful volatility dynamics. Nonetheless, given the poor fore-casting performance of ARCH models reported in a number of recent studies,the question remains as to whether ARCH effects are significant at the high-est frequencies. This section documents, to the contrary, that the ARCH fea-


tures exert a pronounced and systematic impact on the high-frequency volatilityprocess. In addition, we show that the forecasting performance of volatilitymodels is much better than the recent evidence suggests. The key point isthat these studies rely on daily returns to gauge the realized return vari-ability. These measures are, however, extremely noisy, and when improvedmeasurements are obtained from intraday data, the forecast performanceimproves dramatically.

For concreteness, we explore the relation between one-step-ahead volatil-ity forecasts generated by an MA(1)-GARCH(1,1) model of daily returns andalternative measures of return variability based on intraday data.3 The GARCHmodel is estimated from daily data over the longer sample period. The as-sociated estimates of the conditional standard deviation for each day of ourhigh-frequency sample are depicted in Figure 1. Volatility starts out at ahigh level, and consistently declines over the initial one and a half months,followed by a more stable level over the remainder of the sample. However,even the latter period is characterized by sudden bursts of volatility that die

3 Although the GARCH(1,1) model is not necessarily the preferred model, it does represent asimple and popular model that provides a reasonable approximation to the second-order depen-dency in the series (see, e.g., Baillie and Bollerslev (1989)).

Figure 1. Daily GARCH(1,1) volatility forecasts. The figure plots the one-step-ahead con-ditional standard deviation forecasts from an MA(1)-GARCH(1,1) model for the daily deutschemark–dollar spot exchange rate from October 1, 1992 through September 30, 1993, for a totalof 260 nonweekend days. The model is estimated with data over the longer sample period fromMarch 14, 1979 through September 29, 1993.


out only gradually. Finally, there is an apparent surge in volatility at the endof the sample. This overall development is broadly consistent with the dra-matic events surrounding the European Monetary System (EMS) over thesample period.4

To discuss the properties of alternative (ex post) volatility measures, it isuseful to contemplate an explicit model of intraday returns. Suppose thatthe exchange rate is determined by

d log~Pt! 5 mt{dt 1 st{dWt ,

where t $ 0, Wt is a standard Brownian motion with unit variance per day,and the instantaneous mean, mt, and volatility, st, may be governed by sep-arate stochastic processes. Much of modern asset pricing theory is cast interms of such continuous time diffusions. In the notation for the discretelysampled intraday returns defined above, Rt,n [ log~Pt1n0N! 2 log~Pt1~n21!0N!,where t 5 1,2, . . . ,T, and n 5 1,2, . . . , N. In empirical applications to high-frequency data, it is often assumed that the mean return is constant,

E~Rt, n! 5 mt1n0N 5 m,

while time variation in the corresponding volatility process is allowed,

E6Rt, n 2 m6 5 c{st1n0N ,

where c 5 ~p02N !102, and m is approximately zero. One common approachused for evaluation of daily (or lower) frequency volatility estimates, say [st,relies on direct comparison with the corresponding realized absolute re-turns, ~t 5 1,2, . . . ,T !,

4 In early September 1992, the Finnish markkaa gave up its peg to the main Europeancurrencies, and later that month the British pound and Italian lira left the EMS, which limitedexchange rates, through the European Rate Mechanism (ERM), to fluctuate by only 2.25 per-cent versus each other. This created intense speculation that other currencies would leave theEMS, and the volatility in October 1992 reflects the repercussions of these events in the DM–dollar market. The more dramatic episodes include the abolition of the Swedish krona peg on11019, the 6 percent devaluation of the peseta and the escudo on 11023, and the abolition of theNorwegian krone peg on 12010. By Christmas, this round of turmoil had been weathered, butuncertainty arose again during a speculative attack on the Irish punt in late January. The puntwas devalued by 10 percent on 01030, and the market remained unsettled for most of Febru-ary. Market sentiment focused on the willingness of the Bundesbank to support the weakercurrencies by loosening its monetary policy. In fact, ERM tensions were reduced by a Germaninterest rate cut on 02004. Later, the peseta and escudo devalued again, on 05013. This decisionmay have been associated with the upcoming vote, in Denmark, regarding the country’s par-ticipation in the Maastricht treaty and the EMS, but the popular verdict, on 05018, came out infavor of the treaty. The final bout of ERM-related volatility occurred during the latter threeweeks of July, but came to a dramatic halt with the announcement, on 08001, of a widening ofthe ERM band from 2.25 percent to 15 percent for all currencies except the Dutch guildervis-à-vis the DM.


6Rt6 5 * (n51

N

Rt, n* 5 6log~Pt! 2 log~Pt21!6. (1)

Studies adopting this approach include Cumby, Figlewski, and Hasbrouck(1993), Figlewski (1995), Jorion (1995), and West and Cho (1995), amongothers. However, realized absolute or squared daily returns provide a verynoisy measure of the underlying latent volatility. For example, the price mayfluctuate rather wildly, but nonetheless end up close to the opening price,thus (falsely) signaling a low volatility state. A richer measure for volatilitymight instead be based on the sum of the intraday absolute returns, i.e.,

(n51

N

6Rt, n6. (2)

The measure in equation (2) is referred to as the cumulative absolute returnsin the discussion below.5

Under simplifying assumptions it is readily shown that the return vari-ability measure provided by equation (2) is much more efficient than the onein equation (1); see, e.g., Appendix A.6 The practical implication of this resultis illustrated in Figure 2, which displays the two alternative volatility mea-sures along with the corresponding forecasts from Figure 1.7 The weak re-lation between the GARCH forecasts and the absolute return measure inequation (1) is evident in Figure 2a. The daily absolute returns are scatteredalmost arbitrarily around the predicted values, reflecting the inherent noisein daily returns. Table I underscores the point. The sample correlation be-tween the one-step-ahead GARCH volatility forecasts and two differentex post measures of the absolute and the squared daily returns are disturb-ingly low, attaining a maximum of 0.107.8 Clearly, a regression of the ex post

5 A similar measure is used by Hsieh (1991) in calculating daily stock return standard de-viations from fifteen-minute returns. There also is a large literature attempting to extract ad-ditional information about volatility from sources other than the daily returns; for example,Garman and Klass (1980), Parkinson (1980), and Rogers and Satchell (1991) explored the in-formation content in daily observations on high and low prices, while Latané and Rendleman(1976), Day and Lewis (1992), Canina and Figlewski (1993), Jorion (1995), and Xu and Taylor(1995) studied the implied volatility extracted from option prices, and Clark (1973), Epps andEpps (1976), Tauchen and Pitts (1983), Lamoureux and Lastrapes (1990a), Gallant, Rossi, andTauchen (1992), Andersen (1994, 1996), and Jones, Kaul, and Lipson (1994) investigated trad-ing volume.

6 As mentioned earlier, the Appendix may be obtained from the Journal of Finance web site.7 Note that the GARCH volatility estimates rely solely on the preceding squared daily re-

turns and the parameter estimates obtained over the longer sample. Because these parameterestimates are largely unaffected by the realization of returns over the final year of the sample,the volatility estimates are effectively one-step-ahead volatility forecasts based on prior dailyreturns only.

8 The results are robust to the exclusion of holidays. Calculating the correlation between 6Rt6and the GARCH volatility estimate for nonholidays, rather than for the full sample, results inchanges to the third decimal of the correlation number only.


a

b

Figure 2. Daily GARCH(1,1) volatility forecasts versus ex post return variability mea-sures. The figures plot the conditional return standard deviation forecasts from an MA(1)-GARCH(1,1) model for the daily deutsche mark–dollar returns from October 1, 1992 throughSeptember 29, 1993, along with the corresponding realized absolute daily returns (Figure 2a)and the corresponding cumulative absolute five-minute returns (Figure 2b). All series havebeen normalized to average unity over the one-year sample.


volatility measure on the GARCH forecasts has negligible explanatory power,with an explained variability of, at best, approximately (0.107)2 ' 1.1 per-cent. Given this evidence and the inadequacies of ARCH models when ap-plied directly to intraday returns, it is perhaps understandable that manystudies ignore such volatility estimates.

The fallacy of this approach, however, is evident from Figure 2b. The cu-mulative absolute returns from equation (2) are intimately related to theGARCH volatility predictions. The first two columns of Table I reinforce thisconclusion. Over the annual sample, the correlation between the forecastsand the cumulative absolute returns is as high as 0.672. In other words,about (0.672)2 ' 45.2 percent of the variation in the sum of absolute intra-day returns is predicted by the daily forecasts generated by a simple GARCHmodel.9 Furthermore, this variation is at the daily level. It is impossible toexplain this phenomenon by the intraday volatility pattern since this is an-

9 This R2 goes beyond 50 percent if simple adjustments are made for holidays with predict-ably low return volatility.

Table I

Ex Post Correlations between Forecasts of the DailyDeutsche Mark–Dollar Return Standard Deviation (Panel A)

or the Daily Return Variance (Panel B) with Alternative Measuresof the Ex Post Return Variability

The daily return standard deviation and variance for each weekday of the one-year sample, Oc-tober 1, 1992 to September 29, 1993, is obtained from a MA(1)-GARCH(1,1) model estimated usingdaily data on the deutsche mark–dollar (DM–$) spot exchange rate over the longer sample periodfrom March 14, 1979 through September 29, 1993. The measures of ex post return variability forthe first two entries in Panel A, (n51

N 6Rt, n6 and ~(n51N Rt, n

2 !102, and the first entry in Panel B,(n51

N Rt, n2 , are constructed from percentage returns based on interpolated five-minute logarithmic

average bid–ask quotes for the DM–$ spot exchange rate. Quotes from Friday 21:00 GMT throughSunday 21:00 GMT are excluded, resulting in a total of 74,880 return observations. The last twoentries in each of the panels, 6(n51

N Rt, n6 and 6Rt6, and ~(n51N Rt, n!2 and Rt

2, respectively, are basedon ex post return variability measures constructed from daily continuously compounded DM–$returns over the one-year sample. The returns denoted Rt are calculated from the spot exchangerate observed at 12:00 GMT, consistent with the definition used for the longer daily sample; thepreceding entries use the exchange rates observed at 21:00 GMT, which is consistent with the def-inition of the trading day used for the five-minute return sample.

Panel A: Gaussian MA(1)-GARCH(1,1) estimates of st

(n51N 6Rt, n6 ~(n51

N Rt, n2 !102 6(n51

N Rt, n6 6Rt6

0.672 0.618 0.046 0.086

Panel B: Gaussian MA(1)2GARCH(1,1) estimates of st2

(n51N Rt, n

2 ~(n51N Rt, n!2 Rt

2

0.660 0.066 0.107


nihilated when aggregated over the entire trading day. Thus, ignoring theARCH volatility forecasts implies that a large component of predictable re-turn variability is excluded from the high-frequency analysis. Clearly, a mis-leading picture may emerge if we fail to control for this source of commonvariation across the intraday returns.

B. Calendar Effects

Although there is very little evidence of predictability in the conditionalmean of the five-minute DM–$ returns, the series displays pronounced in-traday volatility and activity patterns.10 Figure 3 depicts the average abso-lute return for each five-minute interval across all 260 weekdays in oursample. The initial observation corresponds to the interval ending at 21:00

10 There is evidence of weak negative first-order autocorrelation, most likely induced by spreadpositioning of dealers attempting to correct inventory imbalances by posting quotes that attractcustomers on one side of the market only; see, e.g., Müller et al. (1990), Bollerslev and Domow-itz (1993), and Zhou (1996). This explanation is confirmed by the analysis of actual transactionprices over seven hours in Goodhart, Ito, and Payne (1996).

Figure 3. Intraday volatility pattern. The figure plots the average absolute five-minutedeutsche mark–dollar (DM–$) return for each five-minute interval, starting with the interval20:55–21:00 GMT and ending at 20:50–20:55 GMT. The returns are calculated from inter-polated five-minute logarithmic average bid–ask quotes for the DM–$ spot exchange rate overthe October 1, 1992 to September 29, 1993 sample period. Quotes from Friday 21:00 GMTthrough Sunday 21:00 GMT are excluded, resulting in a total of 74,880 return observations. All260 weekdays are employed in calculating the averages.


GMT, and the last observation represents the interval 20:50–20:55 GMT.Thus, our week originates Monday morning in the Pacific segment wheretrading is dominated by banks located in Wellington and Sydney. Tradingvolume and return volatility is rather subdued at this hour. There is a sig-nificant jump in (average) volatility at 0:00 GMT, or 9 a.m. Tokyo time, cor-responding to the simultaneous opening of trading in a number of financialmarkets, including the Tokyo foreign exchange interbank market and mar-kets for U.S. debt securities. At this point, the market must interpret inno-vations to U.S. bond yields that have occurred since the close of U.S. tradingand absorb any customer orders that have accumulated overnight at autho-rized currency-dealing banks in Japan.11 Although yen–$ dealings comprisethe largest portion of the Asian foreign exchange market, the yen–$ andDM–$ markets are intimately linked through a triangular arbitrage rela-tionship. Thus, it is perhaps not surprising that the effects of the Tokyomarket opening resemble those documented for equity markets by Wood,McInish, and Ord (1985) and Harris (1986). During lunch, 3:00–4:30 GMT,the Tokyo segment shuts down and the overall market typically approachesa standstill. This results in another market opening effect immediately there-after. Ignoring this lunch effect, we may loosely identify a u-shaped patternin volatility over the Asian segment, with the latter part leading into theEuropean segment at 6:00 GMT. Volatility is notably higher during Euro-pean trading, which remains active until about 15:00 GMT. This is to beexpected, as it constitutes the most active trading period and more relevanteconomic news may hit the market during this part of the daily cycle. Al-though the rough outlines of a u-shape are again visible,12 the latter part ofthe pattern may, as before, reflect an overlap in market activity: first the Asianmarket coexists with the European, and later, between 12:00 and 15:00 GMT,the two most active centers trade simultaneously as it is afternoon in Londonand morning in New York. Finally, after the close of the London market, vol-atility displays a monotonic decline until it reaches the plateau associated withthe Pacific segment. There are thus no signs of elevated volatility when trad-ing closes down in New York. Hence, although volatility increases when eachof the main regional segments becomes active, there is no direct evidence ofenhanced volatility associated with the termination of regional trading.13 Thisoverall pattern is consistent with the evidence reported in Baillie and Boller-

11 Prior to December 1994, The Committee of Tokyo Foreign Exchange Market Customs pro-hibited all authorized foreign exchange trading in Japan prior to 9 a.m., between 12:00–1:30p.m., and after 3:30 p.m. local time (see Ito, Lyons, and Melvin (1996)).

12 We later demonstrate that the distinct peaks, at exactly 12:30 and 13:30 GMT, are causedby price movements associated with the release of U.S. macroeconomic news at 8:30 EasternStandard Time (EST).

13 Hsieh and Kleidon (1996) show that volatility computed from quotes specific to a givenregion may display a u-shape for reasons unrelated to informed trading. Because regional quot-ing intensity is low at the early and late stages of regional trading, market volatility is pri-marily determined by quotes emanating from the more active segments, rendering the regionalu-shape irrelevant. However, if all other regions display thin quoting activity at this point intime, the regional pattern can impact the properties of returns computed from quotes on theoverall market. This provides an alternative explanation of the Tokyo market opening effect.


slev (1991), Harvey and Huang (1991), and Dacorogna et al. (1993). We nowturn to a discussion of the other systematic calendar features prevalent in thehigh-frequency returns.

Although there generally is a close coherence between the naive one-step-ahead volatility forecasts from the daily GARCH model and the cumulative ab-solute return volatility measure depicted in Figure 2b, there are a few dramaticdeviations, most notably exemplified by the trading days 62 and 67. These areChristmas Day and New Year’s Day, and both have close to zero quote activity,resulting in imputed intraday returns of near zero. Effectively, they are “week-ends,” as the low activity renders the intraday volatility computation mean-ingless. A similar, albeit weaker, manifestation of a low quoting intensity is atwork on other U.S. holidays throughout the sample. The days 41, 98, 137–138,173, 198, and 243, representing Thanksgiving, President’s Day, Easter, Me-morial Day, July 4, and Labor Day, are prominent examples. There are also in-stances of failures in the data transmission that cause gaps of several hours inour intraday time series. The most noticeable manifestation of this phenom-enon is for day 258. The subsequent analysis explicitly controls for such spu-rious breaks in the volatility process.

A second type of calendar effect often recognized in high-frequency returnsis day-of-the-week dependencies. The apparent need to allow for such effectsis illustrated in Figure 4, where a set of two-hourly dummies is estimatedalong with dummies for each of the weekdays. Mondays appear the leastvolatile, while Thursdays and Fridays are the most volatile.

Third, the GMT time scale used in Figure 3 is dubious due to the obser-vance of Daylight Saving Time in both North America and Europe. If thedaily cycles of economic activity and trading in the different regions areunderlying determinants of the intraday pattern, then it should differ acrossthe Summer Time and Winter Time regimes. Figure 5 supports this conjec-ture. The volatility pattern appears translated leftward by exactly one hourbetween 6:00 and 21:00 GMT (the European and North American segments)during the U.S. Summer Time regime.14

Finally, motivated by the apparent importance of market openings andclosures, we also consider the possibility that volatility behaves differentlyin periods leading into, or out of, such market closures. In particular, we findthat Friday evenings and Monday mornings appear different from the iden-tical periods on other weekdays, and the following analysis consequentlycontrols for both of these effects.

C. Macroeconomic Announcement Effects

Figure 6 suggests that U.S. announcements released at 8:30 Eastern Stan-dard Time (EST), or 12:30 GMT, are the source of the previously observedvolatility spikes during the U.S. Summer Time regime. It displays the in-

14 As detailed in the Appendix (on the Journal of Finance web site), we effectively delete theTokyo lunch period by artificially assigning a low return to intervals between 3:00 and 4:45GMT, thus causing the volatility pattern to appear rectangular over this period. These obser-vations are further “dummied” out in the formal regression analysis conducted below.


traday volatility pattern for Summer days that contain scheduled announce-ments on U.S. macroeconomic data, including the Employment Report, theMerchandise Trade Deficit, the Producer Price Index (PPI), Durable Goods,estimates and revisions to quarterly Gross Domestic Product (GDP), RetailSales, Housing Starts, Leading Indicators, and Jobless Claims. It is appar-ent that the releases induce quite dramatic price adjustments. However, al-though there are signs of elevated volatility for several hours, the main impactseems to be gone within 10–20 minutes. Similar effects are evident for an-nouncements at 13:30 GMT during the U.S. Winter Time regime (not dis-played). These findings are consistent with the observation of heightenedreturn volatility on days with macroeconomic announcements noted by, e.g.,Harvey and Huang (1991) and Ederington and Lee (1993).

Table II displays the 25 largest absolute five-minute returns over the sam-ple, and indicates whether any economic or political events may be identifiedas contributors to the abrupt price change. The latter exercise is, of course,subjective. Nonetheless, the evidence is striking, with the 7 largest, and 15of the 25 largest, absolute returns directly associated with the release ofeconomic news in the same or the immediately preceding interval. Amongother events that seemingly induced “jumps” in the DM–$ exchange rate

Figure 4. Daily and weekly volatility patterns. The figure displays the estimated averageabsolute five-minute deutsche mark–dollar (DM–$) returns obtained from a regression on two-hour and day-of-week dummies. The returns are calculated from interpolated five-minute log-arithmic average bid–ask quotes for the DM–$ spot exchange rate over the October 1, 1992through September 29, 1993 sample period. The two-hour intervals start out at 20:55–22:55GMT and end at 18:55–20:55 GMT.


were the “Russia Crisis,” involving a military confrontation between Yeltsinand hardliners in the Russian Parliament, the plunge of the U.S. stock mar-ket on October 5, the election of Bill Clinton as the next U.S. president, andvarious tumultuous episodes in the ERM, including the widening of the bandto 15 percent, and the floating of the Swedish krona on 11019 that culmi-nated with a devaluation of the peseta and escudo the following weekend.

We conclude that scheduled releases occasionally induce large price changes,but the associated volatility shocks appear short-lived. The reason is prob-ably their one-time character. Market participants may have different infor-mation sets, and thus differ in their interpretation of the news, but themarket typically settles on a new equilibrium price after a brief period ofhectic trading (see, e.g., Goodhart and Figliuoli (1992) and Goodhart et al.(1993)). This is contrary to the often more prolonged impact of unschedulednews. Examples include the Russia Crisis and the Stock Market Plunge whichboth are related to three separate, large innovations, and appear to exertlonger-lasting effects. Announcements may thus constitute news arrivals witha well-defined content and clear-cut termination that endows them with a

Figure 5. Intradaily U.S. Summer and Winter Time volatility patterns. The figure plotsthe average absolute five-minute deutsche mark–dollar (DM–$) return for each five-minuteinterval, starting with 20:55–21:00 GMT and ending at 20:50–20:55 GMT. The returns arecalculated from interpolated five-minute logarithmic average bid–ask quotes for the DM–$ spotexchange rate over the October 1, 1992 through September 29, 1993 sample period. Quotes fromFriday 21:00 GMT through Sunday 21:00 GMT are excluded, resulting in a total of 74,880return observations. The Tokyo lunch period, 3:00–4:45 GMT, is assigned an artificially lowreturn. All 145 weekdays during the U.S. Summer Time and the 115 weekdays during U.S.Winter Time are employed.


particularly short-lived impact, largely unrelated to the strong volatility per-sistence observed at the daily level. Nonetheless, they are sufficiently nu-merous that they induce an appreciable amount of predictable volatility inoverall returns.

III. Modeling the Systematic Features of High-Frequency Volatility

The volatility dynamics of high-frequency foreign exchange returns areinvolved. There are pronounced intraday patterns, highly significant, albeitshort-lived, announcement effects, and standard volatility clustering, or ARCH,effects at lower frequencies. Moreover, the latter cannot exist exclusively atthe lower frequencies, as the aggregation of intraday returns would not beable to accommodate the persistent volatility processes present at the daily

Figure 6. U.S. announcement day volatility. The figure plots the average absolute five-minute deutsche mark–dollar (DM–$) return for each five-minute interval, starting with 20:55–21:00 GMT and ending at 20:50–20:55 GMT for days with regularly scheduled U.S. macroeconomicannouncements during the U.S. Summer Time regime. The returns are calculated from inter-polated five-minute logarithmic average bid–ask quotes for the DM–$ spot exchange rate overthe October 1, 1992 through September 29, 1993 sample period. Quotes from Friday 21:00 GMTthrough Sunday 21:00 GMT are excluded, resulting in a total of 74,880 return observations. TheTokyo lunch period, 3:00–4:45 GMT, is assigned an artificially low return. These days eachcontain at least one release, at 8:30 Eastern Standard Time, of one of the following U.S. mac-roeconomic announcements: the Employment Report, the Merchandise Trade Deficit, the Pro-ducer Price Index, the Advance Durable Goods Report, estimates or revisions to the GrossDomestic Product, Retail Sales, Housing Starts, Leading Indicators, and New Jobless Claims.


level.15 Thus, we stipulate that the volatility process is driven by the simul-taneous interaction of numerous components, some associated with eco-nomic news releases, some with predominantly predictable calendar effects,and some with persistent, unobserved (latent) factors. We demonstrate howformal evaluation of the effects documented in Section II may be performed

15 See the theoretical results regarding temporal aggregation for ARCH in Drost and Nijman(1993) and Drost and Werker (1996), and stochastic volatility in Andersen and Bollerslev (1996b)and Ghysels, Harvey, and Renault (1996).

Table II

Largest Absolute Five-Minute Returns Calculatedfrom the Deutsche Mark–Dollar Spot Exchange Rate

from October 1, 1992 through September 29, 1993The absolute returns are obtained from interpolated five-minute logarithmic average bid–askquotes. Quotes from Friday 21:00 GMT through Sunday 21:00 GMT are excluded, resulting ina total of 74,880 return observations. The 288 intraday returns per 24-hour trading day arenumbered, starting at the interval 20:55–21:00 GMT, and ending with the interval 20:50–20:55GMT. For each interval, we subjectively indicate whether any economic or political event ap-pears to contribute to the large absolute five-minute return.

AbsoluteReturn Date Interval Weekday Event

1.244 10002 188 Friday Employment Report0.897 06004 188 Friday Employment Report0.648 11019 200 Thursday Jobless Claims

Housing Starts0.637 03004 189 Thursday Bundesbank meeting0.581 09003 188 Friday Employment Report0.580 06011 188 Friday Retail Sales

Producer Price Index0.573 10002 189 Friday Employment Report0.530 09021 234 Tuesday Russia crisis0.529 11020 37 Friday ERM turmoil0.527 01029 200 Friday Durable Goods0.517 08002 36 Monday ERM band revision0.510 10005 243 Monday U.S. stock market plunge0.503 09021 233 Tuesday Russia crisis0.501 03005 200 Friday Employment Report0.498 09016 197 Thursday Industrial Output0.494 08031 188 Tuesday Gross Domestic Product0.480 07002 188 Friday Employment Report0.478 10005 240 Monday U.S. stock market plunge0.463 10005 229 Monday U.S. stock market plunge0.458 11004 39 Wednesday U.S. Presidential Election0.455 09021 235 Tuesday Russia crisis0.449 08019 188 Thursday Jobless Claims

Trade Balance0.441 10023 195 Friday ERM turmoil0.439 04022 198 Thursday Bundesbank meeting0.434 10027 200 Tuesday Gross Domestic Product


using a simple two-step procedure, where the final step relies on standardregression techniques.

In full generality, our model takes the following form,

Rt, n 2 ORt, n 5 st, n{st, n{Zt, n (3)

where ORt,n is the expected five-minute return, Zt,n is an i.i.d. mean zero, unitvariance, error term, st,n represents the calendar features as well as the sched-uled announcement effects, and st,n denotes the remaining, potentially highlypersistent, volatility components, that traditionally are captured by ARCH orstochastic volatility models. All the return components are assumed to be in-dependent, and the volatility components are nonnegative; i.e., st,n, st,n . 0for all t, n.16

Without additional restrictions, the components of equation (3) are notseparately identifiable. By squaring and taking logs, we may isolate the cal-endar and announcement effects, st,n, as the sole explanatory variables,

2 log@6Rt, n 2 ORt, n6# 2 log st, n2 5 c 1 2 log st, n 1 ut, n (4)

where c 5 E @log Zt, n2 #, and ut,n 5 log Zt, n

2 2 E @log Zt, n2 #. It is evident that

log st,n, in general, will be stochastic. Each particular release of, say, theEmployment Report is unique, with the figures providing a certain innova-tion relative to consensus forecasts. The price and volatility reaction willreflect this innovation (the news content), the dispersion of beliefs acrosstraders, and probably a host of other market conditions at the time of therelease. In order to capture these dynamic features directly, one must resortto explicit time series modeling based on a wider information set, includingconsensus forecasts, recent return innovations, etc.17 Instead, our goal ismore modest. We merely assume that the (log) volatility response, condi-tional on the type of announcement, the time of the release, and other rel-evant calendar information, has a well-defined expected value, E @log st,n#.This average impact is then governed by purely deterministic regressors. Ofcourse, the innovation, log st,n 2 E @log st,n#, will typically be highly corre-lated for the immediate period following a new release. This will induceserial correlation and heteroskedasticity in the error terms of the regressionthat we develop below, and we are careful to accommodate such features.Finally, we impose the analogous (weak) restriction that log st,n is strictlystationary and has a finite unconditional mean, E @log st,n#.

16 We clearly lose some information by focusing strictly on a model for the imputed five-minute returns. The recent work of Engle and Russell (1997) is motivated by the desire toutilize all of the “ultrahigh” frequency data.

17 Payne (1996) shows that direct estimation of a system containing all three factors is fea-sible, but his stochastic volatility model accommodates only one persistent latent factor. Incontrast, Andersen and Bollerslev (1997b) show that the long-run features of the five-minuteDM–$ return series analyzed here are consistent with a heterogeneous information arrivalinterpretation of the volatility process, but only if the number of latent components, endowedwith relatively strong volatility persistence, is large.


In order to obtain an operational regression equation, we impose someadditional structure. First, we assume that ORt,n is constant and well approx-imated by the sample mean, OR. This is innocuous because the standard de-viation dwarfs the mean return, implying that the inference is not sensitiveto minor misspecification of the conditional mean. Second, we utilize an a pri-ori estimate of the return standard deviation, [st,n, to help control for thissource of systematic volatility movements. Third, we impose a parametricrepresentation on the regressor E @log st,n# of the form f ~ui, t, n!. Since theoryprovides no specific guidelines regarding the shape of the intraday pattern,we allow for a flexible functional form that adapts well to the smooth cyclicalpattern. Our choice is the following

f ~u, t, n! 5 m0 1 (k51

D

lk{Ik~t, n! 1 (p51

P Sdc, p{cosp2p

Nn 1 ds, p{sin

p2p

NnD,

(5)

where Ik~t, n! is an indicator for the event k during interval n on day t, u de-notes the full parameter vector to be estimated, and m0, lk, dc,p, and ds,p arefixed coefficients. Apart from the dummy variables, equation (5) is a Fourierflexible form (FFF) and may be given a semi-nonparametric interpretation.18

Assembling all the pieces, we obtain the operational regression,

[xt, n [ 2 log@6Rt, n 2 OR 6# 2 log [st, n2 5 [c 1 f ~u, t, n! 1 [ut, n (6)

where [c 5 E @log Zt, n2 # 1 E @log st, n

2 2 log [st, n2 # and the error process $ [ut,n% is

stationary.The two-step procedure is now apparent. The first step requires calculat-

ing OR, providing a reasonable estimator of [st,n, and specifying the exact formof the announcement dummies and lag lengths to be included in the regres-sors of equation (5). Thus, the first step provides the observable regressandand regressors for equation (6). The resulting expression constitutes a non-linear regression in the intraday time interval, n, and the event dummies,Ik. It is parameterized by a number of sinusoids (d-coefficients), and dum-mies (l-coefficients). It is estimated, in the second step, by ordinary leastsquares (OLS). We refer to equation (6) and the associated OLS procedure asthe FFF regression. This two-step method is not fully efficient, but, as ar-gued in Appendix B, given correct specification of the first-step FFF regres-sor, the parameter estimates are consistent. An important advantage of the

18 The FFF is introduced by Gallant (1981). The trigonometric terms obey a strict periodicityof one day, as desired. One may add a quadratic function in the intraday interval, n, but theseterms are not significant and thus simply omitted. Allowing for the intraday pattern to dependon the overall volatility level for the day, st, appears important for some markets, but is notsignificant in this context. The more general specification is utilized in Andersen and Bollerslev(1997a).


regression specified in terms of [xt,n, relative to, say, Rt, n2 , is that the log-

transform effectively eliminates the extreme outliers in the five-minute re-turn series, rendering the regression much more robust.

A final issue concerns the proper choice of the first-stage estimator, [st,n. Asimple candidate class may be derived from standard ARCH models, fit atthe daily level. For example, the GARCH(1,1) estimates in Section II.A aredirectly applicable, if one stipulates that this volatility component is con-stant over the trading day. The associated intraday estimates are

[st, n5 [st0N 102. (7a)

Alternatively, the temporal variation in st,n could be ignored altogether, asin the estimator,

[st, n 5 Ts0N 102, (7b)

where Ts denotes the sample mean of [st. In either case, we do not capture thehigh-frequency movements in this component, but, as argued above, the con-sistency of the FFF regression is retained. The advantage of the (constant)estimator (7b) is that it eliminates any generated regressor problem. On theother hand, it does nothing to alleviate the heteroskedasticity. In contrast,the estimator, (7a), does provide a normalization with respect to the strongoverall movements in volatility, which should improve the efficiency of thesecond step procedure, and allow for more accurate volatility forecasts, asdocumented further in Section V below.19

IV. Empirical Results

As in Section II, we report on the empirical findings in three separatesections. The first focuses on calendar, the second on announcement, and thethird on ARCH effects. However, all coefficients are estimated simulta-neously, so the full range of volatility features is controlled for throughout.

A. Calendar Effects

Decisions regarding the treatment of a number of distinct features in thefive-minute return series are necessary prior to estimation of the intradaypattern. We briefly outline our approach, but refer to Appendix C for a more

19 The robustness of the developed FFF regression is worth reiterating. The nature of con-ditional heteroskedasticity is left unspecified, and need not have anything to do with the pre-liminary estimator, [st,n. Likewise, the distributional form for the conditional errors is unspecified,except for the existence of second-order moments. General stochastic dependencies are allowedin both the calendar and announcement effects. The only caveat is a “generated regressor”problem that may arise from the first step estimates of [st,n, which may impart a bias in ourstandard errors (see Pagan (1984)). However, we document below that this problem is negligiblein the current context, given our choice of first-step estimators.


extensive treatment. First, we observe that the extreme slowdown in marketactivity over some holidays as well as the Tokyo lunch period resemblesweekends. Because we aim to characterize the overall, average volatilitypattern, the systematic lack of reliable return observations over a given in-terval during the day is an overriding concern. Consequently, we treat theseepisodes as analogous to weekends and, effectively, eliminate them from thesample. Each Tokyo lunch period, from 12:00 to 1:45 p.m. local time, eachmajor holiday, and each interval associated with a failure in data transmis-sion, are assigned the identical low, positive return, and a dummy variableis introduced to account (perfectly) for the returns over these periods. Thisretains the strict periodicity in the data, while removing any impact fromthese episodes on the inference. Some regional holidays involve only sub-dued, rather than extremely thin, quoting activity, so we introduce a “Holi-day” dummy to accommodate these predictable reductions in volatility. Thereis also some evidence of a slowdown in the periods surrounding the week-ends, i.e., early Monday morning in the Pacific zone, and late Friday after-noon in the North American segment. We accommodate these by constrainedsecond-order polynomials over the corresponding intervals, resulting in tworegression coefficients for each period. The Tokyo market opening effect iscaptured by a single coefficient that allows for a linear decay in the associ-ated volatility burst. U.S. Daylight Saving Time induces a one-hour parallelshift in the intraday pattern over parts of the day, which is readily accom-modated. However, this increases volatility in the earlier part of the (Sum-mer) day, and this is compensated by lower volatility during the now-longerhiatus between the North American and Pacific segments. This is capturedby a restricted second-order polynomial (one free parameter) over the latterpart of the day. We also incorporate day-of-the-week dummies for all week-days except Monday. Finally, we need to select the sinusoids to be includedin the seminonparametric component of equation (4). The removal of theTokyo lunch period facilitates approximation of the intraday pattern by meansof smooth functional, and we obtain an excellent fit using only four sets ofsinusoids; see Andersen and Bollerslev (1997a), Payne (1996), and Kofmanand Martens (1997) for earlier specifications of this form.

We control for four different types of macroeconomic announcements in thissection. The most influential is the Employment Report—the “king of kings”among announcements (Carnes and Slifer (1991))—and it is allowed to abideby its own volatility decay rate. The other significant U.S. announcements areincorporated as “Category I” (more important) or “Category II” (less impor-tant) releases. The former includes GDP and trade balance figures, and Du-rable Goods Orders, while the latter contains the PPI, Retail Sales, HousingStarts, Leading Indicators, Initial Jobless Claims, Factory Orders, and Ger-man M3 figures. Finally, releases following the biweekly Bundesbank meetinghave a major impact, so this effect is also treated separately. Each type of an-nouncement effect is summarized by a single regression coefficient. Interpre-tation of these point estimates is discussed in the next section.

The estimation results for the full system, using the first-step estimator(7a), are recorded in the second column of Table III. All coefficients associ-


ated with the intraday pattern are highly significant, except for the last sineterm.20 As mentioned, the volatility slowdown over the latter part of theSummer days compensates for increased activity earlier in the day due toDaylight Saving Time. The strong market opening effect in Tokyo is note-worthy; the pronounced announcement and holiday effects were expected. Incontrast, the Monday morning effect is insignificant, once all calendar ef-fects are taken into account, and the Friday afternoon effect is at best bor-derline significant. Similarly, there is no indication of a day-of-the-week effect.Although the Friday coefficient is large when judged by conventional OLSstandard errors, the effect is likely an artifact of specific events that hap-pened to occur on Fridays. When evaluated against the robust standard er-ror the effect is decidedly insignificant.

These results justify estimation without the day-of-the-week dummies, asgiven in Table III, column three. The only qualitative difference is that theFriday afternoon effect now is insignificant at the 5 percent level. As a lastrobustness check, we estimate the identical system, imposing the constantdaily volatility factor, (7b). The results in Table III, column four, confirmthat the parameter estimates are largely unchanged and the qualitative fea-tures of the inference unaffected. Thus, the inclusion of [st does not seem togive rise to a practical, generated regressors problem.

The Summer Time intraday volatility pattern, as dictated by the esti-mates in column three, Table III, is displayed in Figure 7. Both the Tokyoopening effect, and the increased volatility during the overlap in the Asianand European and, subsequently, the European and North American seg-ments are apparent. The Monday morning and Friday afternoon effects alsomanifest themselves clearly, in spite of being marginally insignificant. Theexcellent overall fit is evident from Figure 8, which displays predicted andactual average absolute five-minute returns for the corresponding period inthe FFF dimension underlying the estimation. The results for the WinterTime regime are similar.

Arguably, the corresponding fit in the absolute return dimension is a bet-ter gauge of the success of the model. To convert the FFF pattern into ab-solute returns, note that equations (3) through (7) imply

6Rt, n 2 OR 6 5 N 2102{ [st{exp~ f ~u, t, n!02!{exp~ [ut, n02!. (8)

One-day-ahead intraday forecasts, conditional on [st, may therefore be gen-erated by taking the conditional expectation in equation (8), and evaluatingf ~{; t, n! at the estimated u. If we ignore potential correlation between [st andthe transformed error term, we simply have to obtain the unconditional ex-pectation, E @exp~ [ut,n02!#, which in turn may be estimated by averaging thecorresponding expression, exp~ [ut,n02!, over the relevant residuals in the sam

20 The large differences between the heteroskedasticity and autocorrelation consistent stan-dard errors and the OLS standard errors signify the importance of accounting for the effects ofthe strong volatility clustering and outlying observations when conducting the inference.


Table III

Parameter Estimates for the Regression of Logarithmic SquaredDemeaned Five-Minute Deutsche Mark–Dollar Returns

on Deterministic Regressors Capturing Calendarand Announcement Effects

The returns are calculated from interpolated five-minute logarithmic average bid–ask quotesfor the deutsche mark–dollar (DM–$) spot exchange rate from October 1, 1992 through Sep-tember 29, 1993. Quotes from Friday 21:00 GMT through Sunday 21:00 GMT are excluded,resulting in a total of 74,880 return observations. The robust standard errors reflect a Neweyand West (1987) type correction incorporating 289 lags. The regression equation takes the form

2 log6Rt, n 2 OR 6[st, n

5 [c 1 m0 1 (k51

D

lk{Ik~t, n! 1 (p51

4 Sdc, p{cosp2p

Nn 1 ds, p{sin

p2p

NnD 1 [ut, n,

where Rt,n denotes the five-minute returns for interval n on day t, OR the sample mean of the five-minute returns, [st,n is an a priori estimate of the overall daily level of the five-minute return stan-dard deviation, [ut,n is a mean zero error term, and the right-hand side variables represent thedeterministic calendar and announcement regressors. The volatility estimates, [st,n, for intervaln on day t, are obtained from an MA(1)-GARCH(1,1) model fit to a longer daily sample of DM–$spot exchange rates from March 14, 1979 through September 29, 1993. Denoting the daily returnstandard deviation estimate by [st, the daily volatility factor is captured by [st,n [ N 2102{ [st. The“Daily Volatility Excluded” column indicates that N 2102{ Ts is used in place of [st,n, where Ts denotesthe sample mean of [st. During the U.S. Summer Time, the sinusoid regressors are translated left-ward by one hour and an additional restricted second-order polynomial allows for a volatility slow-down between 19:00 and 24:00 GMT. The Ik~t,n! regressors indicate either regular dummy variables(in the case of holidays or weekdays) or a prespecified volatility response pattern associated witha calendar-related characteristic or an announcement. A separate linear volatility decay is al-lowed for the Tokyo open, 00:00–00:35 GMT. Similarly, a restricted second-order polynomial adaptsto the volatility slowdown around the weekends, i.e., early Monday morning, 21:00–22:30 GMT,and late Friday, 17:00–21:00 GMT (U.S. Winter Time) or 16:00–21:00 GMT (U.S. Summer Time).Finally, the volatility decay pattern following announcements is restricted to last one hour (13 in-tervals), except for the Employment Report pattern which lasts two hours (25 intervals). All of theresponse patterns are approximated by a third-order polynomial restricted to reach zero at theend of the response horizon. The announcement coefficients measure the extent to which the ab-solute returns load onto this pattern following the announcement. Category I comprises U.S. an-nouncements on GDP, the trade balance, and durable goods, and Category II covers U.S. releasesof PPI, retail sales, housing starts, leading indicators, jobless claims, and factory orders, and theGerman M3 figures. Robust t-statistics are given in brackets and regular OLS t-statistics are inparentheses.

Parameter Full SystemDay-of-Week

Effect ExcludedDay-of-Week,

Daily Volatility Excluded

m0 1 [c 21.77 21.76 21.85[232.8] [269.2] [256.3](279.4) (2155.6) (2162.0)

dc,1 20.12 20.13 20.13[24.41] [24.58] [24.78](28.27) (28.62) (28.77)

dc,2 20.13 20.13 20.13[24.93] [25.09] [25.10](28.16) (28.30) (28.26)

dc,3 20.28 20.28 20.29[211.8] [212.0] [211.4](218.4) (218.5) (218.5)


Table III—Continued




dc,4 0.14 0.14 0.14[8.10] [8.01] [8.10]

(10.6) (10.6) (10.6)

ds,1 20.62 20.62 20.62[224.1] [223.8] [223.4](238.6) (238.5) (238.4)

ds,2 20.21 20.21 20.21[210.4] [210.2] [210.2](214.3) (214.1) (214.0)

ds,3 0.17 0.18 0.17[8.64] [8.76] [8.55]

(11.9) (12.1) (11.8)

ds,4 20.01 20.01 20.01[20.68] [20.46] [20.68](20.91) (20.62) (20.94)

Summer 21.14 21.15 21.08slowdown [25.91] [25.95] [25.06]

(210.6) (210.7) (29.93)

Tokyo 0.59 0.58 0.59opening [8.96] [8.91] [9.06]

(9.81) (9.76) (9.76)

Holiday 20.698 20.712 20.703[25.76] [26.28] [26.87]

(213.86) (215.25) (214.93)

Employment 1.755 1.746 1.739Report [10.38] [10.47] [8.82]

(11.11) (11.09) (10.95)

Category I 0.997 0.991 0.992announcement [7.23] [7.28] [7.48]

(8.35) (8.33) (8.26)

Category II 0.627 0.620 0.619announcement [6.71] [7.03] [6.89]

(8.64) (8.65) (8.56)

Bundesbank 1.465 1.457 1.492meeting [6.20] [6.20] [6.43]

(10.01) (9.99) (10.13)

Monday 20.301 20.368 20.529early [20.26] [20.32] [20.45]

(20.36) (20.44) (20.63)

0.001 0.069 0.208[0.001] [0.047] [0.14](0.001) (0.065) (0.19)

Friday 20.609 20.412 20.437late [22.04] [21.43] [21.39]

(23.36) (22.37) (22.49)

0.068 0.011 0.017[0.49] [0.08] [0.12](0.88) (0.14) (0.22)


ple.21 The unconditional volatility forecasts may be obtained in identical fash-ion, except that Ts would be used in place of [st. This resulting (unconditional)pattern for the Summer Time regime is displayed in Figure 9, and con-trasted to the actual average absolute returns. While the more pronouncedsensitivity to outliers renders the actual average pattern somewhat jagged,the overall fit is very good.

We end the section by assessing the economic significance of the estimatedFFF coefficients. The point estimates associated with regular dummy vari-ables in equation (5) are readily interpreted. For example, a coefficient ofunity is tantamount to the addition, in equation (8), of a multiplicative fac-tor of exp(102) ' 1.65. Thus, volatility for the corresponding interval in-creases by about 65 percent. Consequently, the holiday factor amounts toexp(20.71202) ' 0.700, or a reduction in volatility of about 30 percent. Thiseffect applies uniformly to each interval covered by the Holiday dummy. Be-yond less important U.S. “holidays,” such as Veterans Day and weekdaysbetween Christmas and New Year’s Day, these also include regional holidaysin Tokyo, Wellington, Sydney, and London.

Assessment of the remaining calendar and announcement effects is morecomplicated because the regressors are not simple indicators, but involveprespecified dynamic response patterns. In particular, assuming that eventk impacts volatility over Nk intervals, the implied set of regressors are

(i50

N

l~k, i!{Ik~t, n 2 i!.

21 Note that any correlation would enhance the predictive power of the daily volatility factor.Thus, the assessment of the explanatory power provided by [st in this context may be deemed aconservative estimate of its true predictive value.

Table III—Continued




Tuesday 20.065[20.95] — —(22.17)

Wednesday 0.006[0.08] — —(0.19)

Thursday 0.050[0.74] — —(1.65)

Friday 0.096[1.31] — —(2.99)


If the announcement affects volatility for an hour or two, there are 13 or 25separate event-specific coefficients to estimate. Given the limited number ofoccurrences of each event and the inherent noise in the returns process, thisis highly inefficient. Instead, we impose a reasonable decay-structure on thevolatility response pattern, and simply estimate the degree to which theevent “loads onto” this pattern, by imposing l~k, i! 5 lk{g~i!, i 5 0,1, . . . , Nk,where g~i! dictates the prespecified pattern. Hence, exp~lk{g~0!02! signifiesthe immediate response of the absolute returns, while the response at theith lag equals exp~lk{g~i!02!. The corresponding cumulative response mea-sure is naturally defined by

M~k! 5 (i50

NkFexpSlk{g~i!

2 D 2 1G. (9)

Figure 7. Flexible Fourier form fit. The figure graphs the fit to the average logarithmic-squared, normalized, and demeaned five-minute deutsche mark–dollar (DM–$) returns acrossthe 24-hour weekday trading cycle during U.S. Summer Time. The returns are calculated frominterpolated five-minute logarithmic average bid–ask quotes for the DM–$ spot exchange rateover the October 1, 1992 through September 29, 1993 sample period. Quotes from Friday 21:00GMT through Sunday 21:00 GMT are excluded, resulting in a total of 74,880 return observa-tions. The interval starts with 20:55–21:00 GMT and ends at 20:50–20:55 GMT. The Tokyolunch period, 3:00–4:45 GMT, is artificially assigned low returns, so this part of the pattern isnot estimated. The fit is based on four sets of sinusoids, dummies for the Tokyo open period,00:00–00:35 GMT, and constrained second-order polynomials for early Monday and late Friday,as well as the latter part of the U.S. Summer Time trading day.


This nonlinear function of the event-specific loading coefficient, lk, reflectsthe impact over the entire response horizon expressed as a multiplicativefactor scaled in units of average volatility per interval over the period. TheTokyo market opening, for example, has an immediate response coefficient of0.65 and a cumulative response measure of 2.12, implying that volatilityjumps by 65 percent at 9 a.m. Tokyo time, while more than twice the usualvolatility of a five-minute interval is added over the span of the half-hourresponse horizon. However, volatility is low at this point in the trading cycle,averaging about 0.025 percent per interval, so the full impact is only around0.053 percent. Because the (median) cumulative absolute return is about9 percent over our sample, this constitutes less than 0.6 percent of the re-turn variability for a typical day. Although the effect is pronounced and ro-bust, and market observers and traders clearly recognize it, it is thus arguablyof limited overall economic importance. A similar calculation shows the eco-

Figure 8. Average intradaily log-volatility fit. The figure graphs the fit to the averagelogarithmic-squared, normalized, and demeaned five-minute deutsche mark–dollar (DM–$) re-turns across the 24-hour weekday trading cycle plotted against the corresponding average sam-ple values. The returns are calculated from interpolated five-minute logarithmic average bid–ask quotes for the DM–$ spot exchange rate over the October 1, 1992 through September 29,1993 sample period. Quotes from Friday 21:00 GMT through Sunday 21:00 GMT are excluded,resulting in a total of 74,880 return observations. The GMT axis starts with the 20:55–21:00GMT interval and ends at 20:50–20:55 GMT. The Tokyo lunch period, 3:00–4:45 GMT, is arti-ficially assigned low returns, so this part is not fitted. The fit is based on four sets of sinusoids,dummies for the Tokyo open, 00:00–00:35 GMT, and constrained second-order polynomials forthe latter part of the U.S. Summer Time trading day, as well as early Monday and late Friday.The latter “weekend effects” are not indicated on the figures. The Summer Time average isbased on 145 weekdays.


nomic significance of the early Monday effect to be negligible. The first fewintervals have an estimated 14 percent reduction in volatility, but the totaleffect amounts to about 0.38 percent of the daily cumulative absolute re-turns. In contrast, the late Friday slowdown exerts a considerable effect.Due to Daylight Saving Time, separate estimates are obtained for Summerand Winter, but the reduction in volatility over the last interval of the day is31 percent in both cases, with a cumulative impact of 3 to 4 percent at thedaily level.

B. Announcement Effects

This section reports on our estimation of the volatility responses associatedwith regularly scheduled macroeconomic announcements in the United States,Germany, and Japan. Extensive experimentation reveals the qualitative fea-

Figure 9. Average intraday absolute return fit. The figure graphs the fit to the averageabsolute five-minute deutsche mark–dollar (DM–$) returns across the 24-hour weekday tradingcycle plotted against the corresponding average sample values. The returns are calculated frominterpolated five-minute logarithmic average bid–ask quotes for the DM–$ spot exchange rateover the October 1, 1992 through September 29, 1993 sample period. Quotes from Friday 21:00GMT through Sunday 21:00 GMT are excluded, resulting in a total of 74,880 return observa-tions. The GMT axis starts with the 20:55–21:00 GMT interval and ends at 20:50–20:55 GMT.The Tokyo lunch period, 3:00–4:45 GMT, is artificially assigned low returns, so this part is notfitted. The fit is based on a Flexible Fourier Form regression of logarithmic-squared, normal-ized, and demeaned returns onto four sets of sinusoids, dummies for the Tokyo open, 00:00–00:35 GMT, and constrained second-order polynomials for the latter part of the U.S. SummerTime trading day, as well as early Monday and late Friday. The latter “weekend effects” are notindicated on the figures. The Summer Time average is based on 145 weekdays.


tures of the average volatility impact to be remarkably similar across an-nouncements, and well approximated by third-order polynomials constrainedto reach zero at a one-hour horizon. In order to allow for simultaneous esti-mation of the multiple effects, we adopt this pattern as a universal format forthe g~i! sequence. The announcements load onto the pattern in accordance withthe logic underlying equation (9), except that a few releases, notably the Em-ployment Report, follow elongated versions, so that their response horizons ex-tend beyond one hour. Apart from this, the only source of variation across theestimated response patterns is the announcement-specific loading coeffi-cients, lk.

A summary of the results may be based on the point estimates for theannouncement coefficients in Table III, column three. The table includes allreleases that are highly significant, with categories I and II consolidatingthose that have similar response patterns. The estimated average effectstake the form displayed in Figure 10. For comparison, the figure also in-

Figure 10. Dynamic announcement response patterns. The figure graphs the relativestrength and duration of the estimated dynamic log-volatility response pattern of the five-minute deutsche mark–dollar (DM–$) returns following the release of macroeconomic announce-ments. The returns are calculated from interpolated five-minute logarithmic average bid–askquotes for the DM–$ spot exchange rate over the October 1, 1992 through September 29, 1993sample period. Quotes from Friday 21:00 GMT through Sunday 21:00 GMT are excluded, re-sulting in a total of 74,880 return observations. The response pattern estimates are obtainedfrom a Flexible Fourier Form regression of the logarithmic-squared, normalized, and demeanedreturns onto four sets of sinusoids, dummies for the Tokyo market opening, and constrainedsecond-order polynomials for the latter part of the U.S. Summer Time trading day, as well asearly Monday and late Friday.


cludes an estimated response pattern for the period following the wideningof the ERM band. Because this decision arguably had the same one-shotcharacter as regularly scheduled announcements, with no additional infor-mation to be released subsequently, the market response should share thequalitative features of the standard announcement responses. The remain-ing estimates are invariant to the inclusion of this event.

The relative size of the response patterns in Figure 10 is as expected. Therevision of the EMS band is a major event, and the large and prolonged vol-atility response is no surprise. The ranking of the regular announcements re-flects the fact that they are presorted according to apparent significance. Moreinteresting is the size of the estimated effects. The coefficients displayed in Fig-ure 10 represent l~k!{g~i! for i 5 0,1, . . . ,32 where, e.g., g~0! 5 2.18869 and lk

is given in Table III. For example, the contemporaneous response to an Em-ployment Report is governed by lk{g~0! 5 1.746{2.18869 5 3.822. From equa-tion (10), this is tantamount to a multiplicative impact on the absolute returnof exp(3.82202) 5 6.76, or an instantaneous jump in volatility of about 576 per-cent. The corresponding cumulative response from equation (9) amounts to 27.17.Since a conservative estimate of the expected absolute return during 8:30 to10:30 EST, absent announcement effects, is approximately 0.05 percent per five-minute interval, the overall effect is an elevation of volatility by 27.27{0.05 51.3585 percent. Therefore, we find about a 15 (51.358509.0) percent averageincrease in the cumulative absolute return for trading days that contain a sched-uled Employment Report. Analogous calculations reveal that the instanta-neous volatility nearly triples for Category I announcements, almost doublesfor Category II announcements, and jumps by almost 400 percent followingBundesbank meetings, while the cumulative impact represents an increase inthe daily cumulative absolute returns of about 3.6, 2.0, and 5.1 percent, re-spectively. Of course, the Bundesbank meetings are biweekly rather thanmonthly, so their overall impact, at least over this sample period, is esti-mated at close to two thirds of that of the U.S. Employment Report. Likewise,Categories I and II represent multiple monthly releases, so their combinedimpact is substantial. We again stress that these estimates represent aver-age, or expected, responses. The most surprising releases are associated witha much larger impact. This point is exemplified by the ERM-band widening,which ranks eleventh on the list of large return innovations in Table II. Theevent is estimated to have raised the instantaneous absolute five-minutereturn by 3,000 percent, and to have increased the cumulative absolute re-turn on August 2, 1993, by 36.6 percent. There are announcements withineach of the four categories that are associated with even larger immediateresponses than the ERM-band correction. Thus, some scheduled announce-ments induce truly spectacular bursts of volatility, although the responses,on average, are decidedly less pronounced.

The strict categorization in Table III is adequate for general characteriza-tion of the announcement effects, but clearly the categories cover quite di-verse events. In order to convey more direct information regarding theimportance of each individual type of release, Table IV reports loading coef-ficients for all U.S. and German announcements investigated in the study.


Table IV

Parameter Estimates of Specific Announcements Effects Obtainedfrom Regressions of the Logarithmic Squared Demeaned

Five-Minute Deutsche Mark–Dollar Returns on DeterministicRegressors Allowing for Calendar and Other Announcement Effects.The returns are calculated from interpolated five-minute logarithmic average bid–ask quotesfor the deutsche mark–dollar (DM–$) spot exchange rate from October 1, 1992 through Sep-tember 29, 1993. Quotes from Friday 21:00 GMT through Sunday 21:00 GMT are excluded,resulting in a total of 74,880 return observations. The regression takes the form

2 log6Rt, n 2 OR 6[st, n

5 [c 1 m0 1 (k51

D

lk{Ik~t, n! 1 (p51

4 Sdc, p{cosp2p

Nn 1 ds, p{sin

p2p

NnD 1 [ut, n,

where Rt,n denotes the five-minute returns for interval n on day t, OR the sample mean of thefive-minute returns, [st, n

2 is an a priori estimate of the overall daily level of the five-minutereturn standard deviation, ût,n is a mean zero error term, and the right-hand side variablesrepresent the deterministic calendar and announcement regressors. The volatility estimates,[st,n, for interval n on day t, are obtained from an MA(1)-GARCH(1,1) model fit to a longer

daily sample of DM–$ spot exchange rates from March 14, 1979 through September 29, 1993.Denoting the daily return standard deviation estimate by [st, the daily volatility factor iscaptured by [st,n [ N 2102{ [st. During U.S. Summer Time, the sinusoid regressors are trans-lated leftward by one hour and an additional restricted second-order polynomial allows for avolatility slowdown between 19:00 and 24:00 GMT. The Ik~t, n! regressors indicate either reg-ular dummy variables (for holidays or weekdays) or prespecified volatility response patternsassociated with a calendar feature or an announcement. A separate linear volatility decay isallowed for the Tokyo open, 00:00–00:35 GMT. Similarly, a restricted second-order polynomialadapts to the volatility slowdown around weekends, early Monday morning, 21:00–22:30 GMT,and late Friday, 17:00–21:00 GMT (U.S. Winter Time) or 16:00–21:00 GMT (U.S. SummerTime). The volatility decay pattern following announcements is restricted to last one hour (13intervals), except for the U.S. Employment Report pattern which lasts for two hours (25intervals). All response patterns are approximated by a third-order polynomial restricted toreach zero at the end of the response horizon. The reported coefficients measure the extent towhich the absolute returns load onto this pattern following the announcement. Beyond thespecific announcement under investigation, all of the regressions allow for the independentinfluence of the U.S. Employment Report, the Bundesbank meeting, and category I and IIannouncements. Category I covers announcements on the U.S. GDP, trade balance, and du-rable goods. Category II includes U.S. releases of PPI, Retail Sales, Housing Starts, LeadingIndicators, Jobless Claims, and Factory Orders, and German M3 figures. If the specific an-nouncement under investigation belongs to one of these categories, it is dropped from thecategory. The instantaneous jump in volatility measures the estimated increase in the five-minute absolute return for the interval where the announcement is made; the estimated totalcumulative absolute return induced by the announcement over the assumed response horizonis measured relative to the median cumulative absolute return over the sample of 9.0 percentper day.

Panel A: Important Announcement Effects

AnnouncementCoefficient

[robust t-stat]Instantaneous Jump

in Volatility (%)Impact in Percent

of Daily Cum. Abs. Return

Employment Report 1.75 576 15.1[11.5]

Advance Report on 1.27 303 5.17Durable Goods [5.75]


Table IV—Continued

AnnouncementCoefficient

[robust t-stat]Instantaneous Jump

in Volatility (%)Impact in Percent

of Daily Cum. Abs. Return

Bundesbank meeting 1.46 392 5.11[9.74]

Merchandise Trade 0.889 164 3.12[4.24]

Gross Domestic 0.836 150 2.87Product (GDP) [3.43]

Producer Price 0.703 116 2.31Index (PPI) [3.67]

Retail Sales 0.670 108 2.17[2.86]

German M3 0.872 160 2.13[4.77]

Leading Indicators 0.624 98 1.99[3.55]

Housing Starts 0.515 76 1.59[2.29]

Factory Orders 0.481 69 1.46[2.05]

New Jobless Claims 0.334 44 0.968[3.02]

Japanese Gross 0.600 93 0.949National Product [2.40]

German Gross 0.506 74 0.931Domestic Product [1.43]

Panel B: Less Important U.S. Announcements

Announcement Coefficient Robust t-stat

U.S. Treasury Report 0.338 1.62Consumer Confidence (Conference Board) 0.273 1.20Consumer Price Index (CPI) 0.236 1.02Construction Spending 0.211 0.954Car Sales 0.091 0.709Business Inventories 0.124 0.704Housing Completions 0.070 0.430Import Prices 0.076 0.374University of Michigan Survey 0.043 0.315Current Account Deficit 0.084 0.314Industrial Output0Capital Utilization 0.067 0.282Non-Farm Productivity 0.035 0.154M2 Figures 0.017 0.134Personal Income 0.030 0.102Real Earnings 0.005 0.021Reserve Assets 20.012 20.062House Sales 20.041 20.150Minutes from FOMC Meeting 20.177 20.613Capital Spending Survey 20.261 20.689


These are obtained by treating each announcement in the manner affordedthe Employment Report and Bundesbank meetings in Table III, i.e., we con-trol for all remaining significant announcements while estimating the mar-ginal impact of the release under investigation. All statistically significantreleases are listed in Table IV, Panel A, and ranked according to their esti-mated impact on the cumulative absolute returns. The results largely con-firm our earlier findings. Indeed, the first twelve announcements are theones controlled for throughout in our estimation procedure. The set of sig-nificant U.S. releases also corresponds closely to those identified by Eder-ington and Lee (1993, 1995a, 1995b) and Payne (1996). Of course, we wouldexpect the relative importance of the releases to differ across markets. Forinstance, Ederington and Lee (1993) and Jones, Lamont, and Lumsdaine(1995) find the PPI figures to be almost as important as the employmentreport for U.S. bond market volatility; see also Goodhart et al. (1993) andDeGennaro and Shrieve (1995) for analyses of high-frequency news effects in

Table IV—Continued


NAPM Survey 20.205 20.777Consumer Installment Credit 20.375 21.02Wholesale Sales 20.181 21.06

Panel C. Less Important German Announcements


Wholesale Turnover 0.322 1.56Retail Sales 0.124 0.668Consumer Price Index (all states tallied) 0.072 0.668East German Consumer Price Index 0.122 0.647East German Industrial Orders 0.152 0.630Industrial Orders 0.110 0.465Producer Price Index 0.085 0.423Wholesale Prices 0.054 0.295Current Account 0.032 0.181Consumer Price Index (First State) 0.010 0.051Business Insolvencies 0.002 0.010Employment Report 20.004 20.022Import Prices 20.011 20.049Consumer Price Index (Final) 20.089 20.427East German Employment 20.075 20.438East German Producer Price Index 20.092 20.503Industrial Output 20.176 20.702Capital Account 20.238 21.14East German Industrial Output 20.245 21.18Consumer Price Index (Preliminary) 20.563 21.84


the U.S. dollar–British pound and U.S. dollar–Japanese yen foreign ex-change markets, respectively.22 The overwhelming significance of the twoGerman monetary announcements is also interesting, especially in light ofthe fact that none of the corresponding U.S. monetary announcements haveany explanatory power; for evidence pertaining to earlier periods and otherrates see, e.g., Hardouvelis (1984), Goodhart and Smith (1985), Hakkio andPearce (1985), Ito and Roley (1987), and Thornton (1989). However, it isworth recalling the intense scrutiny of German monetary policy over thesample period due to the frictions in the EMS.23 Moreover, U.S. monetarypolicy was unusually uncontroversial over the period. For example, therewere no changes in the Fed Funds rate over the sample. Only confirmationof our results over a longer sample period will allow us to gauge the robust-ness of these particular findings. Nonetheless, the results are consistent withthe emphasis that the Bundesbank allegedly places on monetary targets asguidelines for its policy decisions.

Table IV, Panel A, also includes the only Japanese release of any signifi-cance, namely the Japanese GNP figures. Since there are only four annualreleases of this statistic, the announcement is of limited overall importance,but the statistical significance is noteworthy. The directional response of theexchange rate is consistent with a strengthening of the dollar on positiveinnovations to the Japanese GNP. It suggests an interpretation that stressesthe U.S.–Japanese trade imbalance. Strong growth in Japan would be con-ducive to imports from the United States, and a shrinkage of the overall U.S.deficit vis-à-vis Japan. However, the small sample precludes any firm con-clusions. For comparison purposes the table also includes the German GDPfigures. These are estimated to be of about the same economic importance asthe Japanese GNP numbers, although the effect is not statistically signifi-cant at the 5 percent level.

The remaining 22 U.S. and 20 German news releases were all individuallyinsignificant, but the mere fact that a majority of the coefficients are posi-tive (15 versus 7 and 11 versus 9, respectively) suggests that on averagethese announcements contribute positively to the DM–$ volatility, althoughthe economic impact in most instances is negligible. The complete listing isgiven in Table IV, Panels B and C.

The qualitative importance of the announcement effects is perhaps bestillustrated by observing that they “explain” the significance of weekdaydummies. A number of previous studies have noted the importance of al-lowing for day-of-the-week effects when modeling daily exchange rate move-

22 Eddelbüttel and McCurdy (1996) and Chang and Taylor (1996) also find that a simplefrequency count of the news headlines on the Reuters screen is positively related to the intra-daily DM–$ volatility, but has low overall explanatory power.

23 For a recent discussion of the Bundesbank monetary policy rules see Clarida and Gertler(1996). In a related context, Peiers (1997) provides an empirical analysis on the role of priceleadership by Deutschebank in the DM–$ interbank market in the two hours surrounding Bundes-bank foreign exchange interventions.


ments; see, e.g., McFarland, Pettit, and Sung (1982, 1987), So (1987), Hsieh(1988, 1989), and Baillie and Bollerslev (1989). Upon running the FFFregression, using the volatility estimates from equation (6), and includingall calendar effects but excluding the announcement effects, we obtain thefollowing coefficients on the weekday dummies for Tuesday through Fri-day: 20.038 [20.54] (21.26), 0.038 [0.53] (1.24), 0.118 [1.68] (3.85), and0.165 [2.19] (5.09), where the square brackets provide robust t-statisticsand the parentheses report standard OLS t-statistics. Thus, ignoring theannouncement effects produces economically large day-of-the-week effects,with Friday having estimated excess absolute returns on the order ofexp( 1

2_ {0.165) 2 1 ' 8.6 percent, and Thursday of exp( 1

2_ {0.118) 2 1 ' 6.1

percent. Moreover, the effect is highly significant based on the conven-tional heteroskedasticity adjusted OLS standard errors, and the Fridayeffect remains significant at the 5 percent level when judged against fullyrobust standard errors. Of course, Table III demonstrates that this resultvanishes, if we account for the announcement effects. The large Thursdayand Friday dummies reflect the clustering of scheduled news releases onthese weekdays. Given the estimates in Table IV, a back-of-the-envelopecalculation indicates the magnitude of the involved effects. For example,Fridays contain all 12 Employment Report releases, as well as 4 TradeBalance, 2 Housing Start, 5 CPI, 3 Retail Sales, 5 PPI, 5 Business Inven-tories, 3 Durable Goods, 3 GDP, 3 Factory Orders, 5 Industrial Output0Capital Utilization, 1 Leading Indicator, 1 Jobless Claims, and 1 Bundesbankmeeting releases over the year. In total, this increases the average cumu-lative absolute returns on Fridays by about 5.4 percent. The unexplainedgap of about 3.1 percent is small, and certainly consistent with randomvariation. In fact, from Table II it is evident that the most influentialreleases of PPI, Retail Sales, and Durable Goods figures happen to occuron Fridays, and, in addition, there are two distinct episodes of “ERM tur-moil” on this weekday. Hence, the enhanced volatility on Fridays isreadily “explained,” which is consistent with the message obtained fromthe robust inference. A similar analysis applies to Thursdays. The Bundes-bank meetings typically take place on this weekday, resulting in 23 re-leases. This combined with 51 Jobless Claims, 6 Trade Balance, 6 FactoryOrders, 5 Retail Sales, 4 PPI, 3 CPI, 3 GDP, and 2 Housing Start Releasesplus numerous minor announcements explains an average elevation ofvolatility on the order of 5.0 percent. The residual 1.0 percent is compara-ble to the implied variation across the first three weekdays, and is clearlyinsignificant.

Consequently, there is no evidence of a day-of-the-week effect. The impli-cation is that volatility forecasts based on such dummies are biased. For in-stance, if there are no scheduled announcements on a Friday, forecasts will tendto be inflated by about 7 to 8 percent, but volatility for a Friday containingjust an Employment Report release, on average, will be underestimated by thesame magnitude. If additional announcements are scheduled for the same Fri-day the downward bias in the forecast is further aggravated.


In summary, macroeconomic announcements have a large impact whenthey hit the market, with the largest five-minute returns over the entiresample readily being identified with such public releases. Clearly, for sensi-ble inference around these periods, it is necessary to control for this effect.However, the induced bursts of volatility are short-lived. As such, the overallsignificance of these announcements for volatility at the daily level is tenu-ous. In fact, the majority of the releases induce average excess cumulativeabsolute returns of approximately, or less than, 5 percent of that for a typicaltrading day. Only the employment report is associated with a substantiallyhigher impact. Section V further explores the significance of the documentedeffects for explaining overall volatility.

C. Longer-Run Volatility Components

A significant finding to emerge from our study is that the high-frequency re-turns contain valuable information for measurement of volatility at the dailylevel. Specifically, the cumulative absolute returns provide a much better expost measure of the underlying daily latent volatility factor than either abso-lute or squared daily returns. These results encourage the development of newand improved techniques for the estimation and prediction of daily or lowerfrequency volatility that explicitly incorporate the information in high-frequencyreturns. In addition, as we show below, the intraday returns provide new in-sights that are of critical importance for the understanding of the lower fre-quency return dynamics.

Given our estimates of the systematic, or deterministic, calendar and an-nouncement effects, we may filter the high-frequency returns to obtain aninnovation process that retains only the purely stochastic components of thevolatility process. If our modeling strategy is warranted, the properties ofthis (residual) return series should be largely void of calendar effects anddisplay the type of volatility dependencies usually associated with ARCH-type processes. To investigate this hypothesis, Figure 11 displays the cor-relogram for the raw absolute five-minute returns, 6Rt,n 2 OR 6, as well as thecorresponding filtered absolute returns, [st, n

21{6Rt, n 2 OR 6. The former, depictedin Figure 11a, is dominated by the strong periodicity at the daily frequencyand does not appear particularly informative.24 Figure 11b, in contrast, fea-tures a strictly positive and slowly declining correlogram. Spikes are visibleat the daily frequencies, but they are minor and do not distort the overallpattern. This may be interpreted as a testimony to the relative success ofour model for st,n in capturing the systematic calendar and announcementeffects. The regularity of the correlogram in Figure 11b compares favorablyto those of similarly filtered absolute returns presented in Andersen andBollerslev (1997a) and Payne (1996). The excellent fit afforded by the hy-

24 Both series are adjusted for missing observations, so that, e.g., the Tokyo lunch hour isremoved. The daily periodicity is even more pronounced when the lunch time observations areretained.


a

b

Figure 11. Absolute return correlograms. The figures display the autocorrelations for de-meaned raw and filtered five-minute absolute returns. The returns are calculated from inter-polated five-minute logarithmic average bid–ask quotes for the deutsche mark–dollar spot exchangerate over the October 1, 1992 through September 29, 1993 sample period. Quotes from Friday21:00 GMT through Sunday 21:00 GMT, along with the Tokyo lunch period, 3:00–4:45 GMT, arenot included, resulting in 267 weekday return observations, for a total of 69,420 five-minutereturns. Additional minor corrections are also made for extremely low quoting activity duringholidays and gaps in the data series. The filtered returns in Figure 11b are obtained by stan-dardizing the raw demeaned absolute returns by the estimated volatility impact of calendar,holiday, and announcement effects.


perbolic decay superimposed in the figures is particularly noteworthy. Thisrate of decay is inconsistent with ordinary ARCH models, and instead pointstoward a fractionally integrated, or long-memory, volatility process, as pro-posed by Baillie, Bollerslev, and Mikkelsen (1996) in the ARCH framework, andHarvey (1994) and Breidt, Crato, and de Lima (1995) within the context of sto-chastic volatility models.25 The estimate of the degree of fractional integra-tion, or d, implied by the fitted hyperbolic decay in Figure 11 equals 0.387, whichis in close accordance with the estimates obtained by semiparametric fre-quency domain methods in Andersen and Bollerslev (1997b) and Henry andPayne (1996).26 Thus, the long-memory characteristics appear inherent to thereturn series, as they manifest themselves, even over shorter time spans. Thissuggests that the source of fractional integration in the volatility is related tothe data generating process itself, rather than induced by infrequent struc-tural shifts as suggested by Lamoureux and Lastrapes (1990b). Thus, once weaccount for announcement and calendar effects, the high-frequency data pro-vide important evidence on the plausibility of two alternative hypotheses thatappear almost observationally equivalent from the perspective of lower fre-quency returns.

V. The Relative Importance of Volatility Componentsat Different Frequencies

Different market participants are concerned with different features of thevolatility process. Market makers, brokers, and money managers engagingin continuous trading or the implementation of dynamic portfolio and hedg-ing strategies are exposed to short-run volatility, and consider informationon this dimension vital. Conversely, more passive investors are mostly con-cerned with lower frequency movements. Likewise, research into the pricemechanism or other market microstructure issues focuses on the extremehigh-frequency movements, but standard asset pricing models typically arespecified and tested at daily or lower frequencies. Although the higher andlower frequency characteristics cannot be entirely independent, the differ-ence in perspective will lead to rather wide discrepancies in the assessmentof the economic significance of the factors that we have explored above. Thissection formally evaluates the impact of each component at both the extremehigh frequency and the daily level.

The FFF framework allows for a direct assessment of the joint and mar-ginal predictive power of each of the three separate components; the dailyvolatility factor, the calendar effects, and the announcement effects. We letthe indicator variable, Is, be unity if the daily (ARCH-based) volatility factorfrom equation (7a) is included in the construction of a given forecast, and

25 The autocorrelations for a fractionally integrated process of order d eventually decay atthe hyperbolic rate of j 2d2l.

26 The reported estimate of 0.387 is obtained from the regression log~ [rj! 5 b0 1 b1 log~ j! 1uj, j 5 5, 6, . . . , 2670, where [rj denotes the sample autocorrelation for the absolute returns,and Zd 5 1

2_ ~ Zb1 1 1!; see Andersen and Bollerslev (1997b) for details.


zero if the forecast is based on a constant daily volatility factor, as in equa-tion (7b). Formally, this component takes the form,

[st, n 5 [st{Is 1 Ts{~1 2 Is!.

Likewise, the indicators Ic, Ia, and Ih signify whether calendar, announce-ment, and holiday effects are accounted for in the volatility forecast. Thecalendar coefficients, fc, include the FFF sinusoids, the Tokyo open, the Day-light Saving Time, the early Monday, and the late Friday regressors, theannouncement effects, fa, signify the contribution of the four announcementregressors from Table III, and the holiday effects, fh, refer to the predictedreduction in volatility associated with the holiday dummy and the control formissing observations. The latter effects were incorporated in all forecasts, sothat this source of predictable return variability would not interfere with theinterpretation of the results. Based on the FFF regressors in equation (5), itis now straightforward to construct a volatility forecast from equation (8),and identify the contribution from each of the three remaining sources ofsystematic variation. In particular, letting the vector of indicator variables,I 5 ~Is, Ic, Ia!, identify a given model configuration, the set of one-day-aheadabsolute return interval forecasts is calculated as

v~I; t, n! 5 c0{ [st, n{expS Zfc~t, n!{Ic 1 Zfa~t, n!{Ia 1 Zfh~t, n!{Ih

2 D, (10)

where Zfc~t, n! 5 fc~ Zu, t, n! and so forth, and Zu is estimated conditional on thecurrent variant of the model, as indicated by I. Thus, the parameters areallowed to vary across the designs in a manner that maximizes the explan-atory power of the specific components for each configuration.

Table V provides the fraction of the total variation in absolute returnsexplained by each forecast. These are given as the R2 from the followingregressions of realized cumulative absolute returns, ~t 5 1, . . . ,T !,

(n51

N

6Rt, n 2 OR 6 5 b0 1 b1{ (n51

N

v~I; t, n! 1 et , (11)

and realized five-minute absolute returns, ~t 5 1, . . . ,T ; n 5 1, . . . , N !,

6Rt, n 2 OR 6 5 b0 1 b1{v~I; t, n! 1 et, n , (12)

on the corresponding volatility forecasts.The results are telling. Consider the first data column in Table V, that

refers to the degree of explained variation in daily cumulative absolute re-turns. The complete model accounts for an impressive 60.6 percent of thetotal variation. Moreover, this number drops only slightly if we remove theannouncement or the calendar components from the forecast. In contrast,


the explained variation drops precipitously when the daily volatility factor isomitted. In fact, the benchmark explanatory power, provided by the holidayeffects alone (8 percent), is only marginally improved by incorporating cal-endar effects (8.3 percent) and only slightly improved when allowing for an-nouncement effects (11.4 percent). In contrast, the daily GARCH volatilityfactor alone explains 57.8 percent. The message is clear. The daily volatilityforecasts capture broader movements in volatility that generally are inde-pendent of calendar effects. This is perhaps not surprising given that theintraday pattern, which accounts for the majority of these features, is anni-hilated when aggregated to the daily level. More striking is the marginalimpact of the announcements at the daily level. Although announcementeffects explain a significant proportion of the return variability over shorterintervals, as also documented in Ederington and Lee (1993), this is not thecase relative to the full 24-hour trading day, which is characterized by fairlylarge fluctuations in the overall level of volatility.27 Finally, we note that thecalendar effects pick up additional explanatory power if day-of-the-week ef-fects are allowed, but remain less important than the announcement effects.This is fully consistent with the weekday dummies substituting (imperfect-ly) for the news releases.

Turning to the last column of Table V, we find that the explanatory powerof the components is reversed when we consider the high-frequency returnvariability. The overall explained variation drops to 15.9 percent, but morerevealing is the fraction explained by the calendar effects alone (8.1 percent)relative to the announcement effects (4.9 percent) and the daily volatilityfactor (3.4 percent). In other words, the intraday pattern accounts for themajority of the explained variation, but the announcements are sufficientlyinfluential, in spite of the relatively few intervals they affect, that they alsoexert an appreciable impact, and, finally, the overall predictable movementsin daily volatility have only a limited, although not negligible, impact at thefive-minute return level.

VI. Concluding Remarks

The volatility process of the DM–$ spot exchange rate market is involved,with entirely new phenomena becoming visible as one proceeds from dailyreturns to high-frequency intraday returns. Nonetheless, it is possible toidentify three general sets of characteristics that govern the systematic fea-tures of the process. At the high-frequency level, the pronounced intradayvolatility pattern is dominant, accounting for an average variation in abso-lute returns of more than 250 percent across the 24-hour trading cycle (afterexclusion of the Tokyo lunch period). At the intraday level, the magnitude ofthis effect overwhelms the predictable changes in volatility captured by, e.g.,

27 Subsample analysis reveals that the explained variation drops when the overall level ofvolatility is more stable. However, the ranking of the effects remains the same across all in-vestigated subsamples.


Table V

Explained Variation (R2) from Regressions of Deutsche Mark–DollarDaily Cumulative Absolute Returns or Five-Minute Absolute

Returns on Alternative Absolute Return ForecastsFor the daily cumulative absolute returns, the regression takes the form

(n51

N

6Rt, n 2 OR 6 5 b0 1 b1 (n51

N

v~I; t, n! 1 et ,

where v~I; t, n! denotes the relevant absolute return forecast for interval n on day t, and et is anerror term. The regressions for the five-minute absolute returns are calculated as

6Rt, n 2 OR 6 5 b0 1 b1{v~I; t, n! 1 et, n .

The five-minute returns are based on interpolated logarithmic average bid–ask quotes for thedeutsche mark–dollar (DM–$) spot exchange rate from October 1, 1992 through September 29,1993. Quotes from Friday 21:00 GMT through Sunday 21:00 GMT are excluded, resulting in atotal of 74,880 five-minute observations. The daily cumulative absolute returns are aggregatedfrom 21:00 GMT to 21:00 GMT the following day. The corresponding one-day-ahead five-minuteabsolute return forecasts are obtained as

v~I; t, n! 5 ~N 2102 @ [st{Is 1 Ts{~1 2 Is!#!{c0{expS Zfc~t, n!Ic 1 Zfa~t, n!Ia 1 Zfh~t, n!

2 D,

where the first term on the right-hand side represents an estimate of the benchmark returnvolatility of the interval, while Zfc~t, n!, Zfa~t, n!, and Zfh~t, n! denote the estimated calendar, an-nouncement, and holiday effects from a regression of normalized, log-squared, demeaned five-minute DM–$ returns on calendar, announcement, and holiday regressors. The functional formof the forecast equation translates the estimates into the absolute return dimension. The indi-cator variables Is, Ic, and Ia signify whether the features associated with a given effect areaccounted for in the construction of a particular forecast. For example, the indicator vector I [~Is, Ic, Ia! 5 ~0,1,1! corresponds to the model where the daily volatility is constant, and calendar(c) and announcement (a) effects are accounted for. Because the holiday effect, Zfh~t, n!, is in-cluded in all of the forecasts, the R2’s reported here exceed the simple correlations given inTable I. Estimates for the time-varying daily return standard deviations over the one-yearsample, [st, are obtained from an MA(1)-GARCH(1,1) model fit to a longer daily sample of DM–$returns covering the period from March 14, 1979, through September 29, 1993. The samplemean of [st is denoted by Ts. The “*” indicates the allowance for day-of-the-week dummies amongthe calendar effects, while they are excluded otherwise.

DesignDaily CumulativeAbsolute Returns

Five-MinuteAbsolute Returns

Complete model 0.606 0.159~Is, Ic, Ia! 5 ~1,1,1!

No announcements 0.579 0.113~Is, Ic, Ia! 5 ~1,1,0!

No calendar effects 0.603 0.084~Is, Ic, Ia! 5 ~1,0,1!

Only daily volatility 0.578 0.034~Is, Ic, Ia! 5 ~1,0,0!

No daily volatility 0.119 0.124~Is, Ic, Ia! 5 ~0,1,1!


ARCH models, which rarely move by more than 25 percent over any 24-hourperiod. Additionally, strong but short-lived announcement effects are preva-lent at the highest frequencies.

Our results verify that the high-frequency calendar and announcementeffects may be estimated efficiently, even without accounting for the broadermovements in daily volatility. On the other hand, real-time decision-makingand the analysis of one-time events require controlling not only for the in-traday pattern and the release of economic or political news, but also for theoverall level of volatility. Furthermore, when analyzing the economic impli-cations of the identified factors, it is evident that the daily volatility factordominates at the daily and lower frequencies. Thus, it might be argued thatthe intraday pattern and announcement effects are of lesser economic im-portance, and that high-frequency data are of interest only for the area ofmarket microstructure.

Any such conclusion, dismissing the importance of intraday return seriesfor broader economic issues, is misleading. First, the high-frequency returnscontain extremely valuable information for the measurement of volatility atthe daily level. Second, the intraday returns reveal that there are significantlong-memory features in the return dynamics. These features are critical forportfolio management and derivatives pricing. Moreover, they are relevantfor the analysis of information transmission and volatility spillover, bothcontemporaneously across markets and intertemporally between the geo-graphical regions of the identical market (see, e.g., Engle, Ito, and Lin (1990),Hamao, Masulis, and Ng (1990), and Hogan and Melvin (1994)). In sum-mary, the information provided by high-frequency returns is valuable to abroad range of issues in financial economics, both within and beyond therealm of market microstructure.

Table V—Continued

DesignDaily CumulativeAbsolute Returns

Five-MinuteAbsolute Returns

Only announcements 0.114 0.049~Is, Ic, Ia! 5 ~0,0,1!

Only calendar effects 0.083 0.081~Is, Ic, Ia! 5 ~0,1,0!

Calendar 1 Day-of-week 0.107 0.083~Is, Ic, Ia! 5 ~0,1,0!*

Only holiday effects 0.080 0.002~Is, Ic, Ia! 5 ~0,0,0!


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